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Technol Econ Smart Grids Sustain Energy (2016) 1: 11DOI 10.1007/s40866-016-0010-5

ORIGINAL PAPER

Investigations on Harmonics in Smart Distribution Gridwith Solar PV Integration

J. V. Desai1 · Pradeep Kumar Dadhich2 · P. K. Bhatt1

Received: 28 January 2016 / Accepted: 25 July 2016 / Published online: 8 August 2016© Springer Science+Business Media Singapore 2016

Abstract Integration of solar PV into the grid poses manychallenges in the power system. One such serious chal-lenge is harmonics penetration into the system. Harmonicsare generated by the solar PV and the associated powerelectronics circuitry. Moreover, the loads connected to thedistribution system are usually nonlinear and harmonic richin nature. Therefore, a lot of harmonics gets introducedinto the system from the source as well from load ends,and thereby affecting the power system performance. Inthis paper, harmonic distortion issues associated with solarPV integration are analyzed considering the limits of IEEE519-1992 standard. The Newton-Raphson algorithm is mod-ified with solar PV integration for harmonic power flowstudy. The formulated approach is employed to determinethe discrete harmonic components, total harmonic distortion(THD) levels, and values of the system power flow vari-ables. The developed approach is tested on a smart radialdistribution feeder and the results show that with solar PVintegration, the harmonic distortion increases above accept-able limits. In order to have a vision of smart grids forproviding clean power supply, the authors feel that there isa serious need to study the issues related to harmonic gener-ation, and further to develop control strategies to eliminatethem.

� P. K. Bhattpramod [email protected]

1 College of Engineering & Technology, Mody University,Lakshmangarh, India

2 Integrated Research and Action for Development, New Delhi,India

Keywords Harmonics · Total harmonic distortion ·Harmonic power flow · Grid integrated solar PV · Smartgrid distribution system

Introduction

The presence of harmonics is unavoidable in a power sys-tem due to the nonlinear characteristics of equipment andconnected loads [1]. Integration of solar PV system furtherintensifies the harmonics in the distribution network. Theseharmonics emanate within the inverter during the normalpower conversion process [2]. The nonlinear behavior ofsolar PV with changing weather condition increases inverterswitching, which injects additional harmonics in the sys-tem [3, 4]. The magnitude and order of harmonics dependon the power inverter technology used, adopted modula-tion technique, method of commutation, existence of highor low frequency coupling transformer, interconnection con-figuration and filters used at the output side of the inverter[5–9].

The interaction between grid components and numberof solar PV units further amplifies the harmonic distortion[10].

The objective of this paper is to analyze the distributionnetwork with solar PV integration, and to study the volt-age/current harmonic distortions at various buses/branches.Paper also deals with the deviation of these distortions fromthe standard IEEE limits [11], thereby emphasizes the needfor developing suitable control strategies to eliminate themin order to maintain the clean power supply. To examinethese issues, the Newton-Raphson algorithm is reformulatedand implemented by including the solar PV and nonlinearloads on the smart radial distribution feeder. The results

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Fig. 1 a Equivalent circuit,Homo junction solar cell. bEquivalent circuit, Solar cellwith impurity recombinationcurrent

(a)

(b) Equivalent circuit, Solar cell with impurity recombination current

Equivalent circuit, Homo junction solar cell

of the harmonic power flow analysis are comprehensivelyanalyzed and the observations are presented.

The paper is organized as follows: The modeling of var-ious power system components in harmonic domain is pre-sented in “Modeling of Power System Components”. Theharmonic analysis and simulation algorithm is discussedin “Harmonic Analysis Algorithm”. Design of smart radialdistribution grid is given in “Design of Smart DistributionGrid System”. “Simulation Results Analysis” presents sim-ulation results analysis and associated discussion on theharmonic distortions. Finally, “Conclusion” concludes thepaper by summarizing the work carried and investigationsmade.

Modeling of Power System Components

For analyzing the issues connected with the harmonics, weneed to develop appropriate models of various power sys-tem components, used in our study. This section presents

the harmonic domain modeling of various power systemcomponents.

Modeling of Solar PV

A PV system exhibits the nonlinear I-V characteristics andintroduces harmonics in the system by itself. An ideal PVcell is modeled as a current source which represents the gen-erated current due to incident light and a parallel diode forp-n junction of PV cell but the model of a real PV cell con-tains additional parallel resistance Rp, represents the currentleakage through the cell and a series resistance Rs, accountsfor an extra voltage drop between the junction as shown inFig. 1a. In an ideal situation, to determine the upper limitof open circuit voltage and the efficiency of solar cell, it isassumed that only radiative recombination takes place. ButIn the actual solar cell, the recombination via impurities pre-dominates as presented in Fig. 1b [12–15]. Furthermore, thepresence of solar array capacitance, as presented in Fig. 2,also increases the voltage ripple and has the dominant effect

Fig. 2 Equivalent circuit withsolar array capacitance

Technol Econ Smart Grids Sustain Energy (2016) 1: 11 of 11 11

Fig. 3 Transformer equivalentcircuit for harmonics studies

on the performance of the switching regulators at higherswitching frequencies [16, 17].

The equation for current and voltage relationship of PVarray is expressed in Eq. 1.

I = Iph − I0

[exp

(q (V + RsI)

NsKT

)− 1

]−

(V + RsI

Rp

)

(1)

Where, Iph : Photo generated current (A) i.e. current gen-erated by the incident light (it is directly proportional tothe sun irradiation), Id : Diode equation (A), I0 : Reversesaturation or leakage current of the diode (A), q: Chargeof electron (1.160217646 ×10−19 C), K: Boltzmann con-stant (1.3806503 ×10−23 J/K), T : Temperature of the p-njunction (◦Kelvin), Ns : Number of cells, Rs : Series resis-tance (�), Rp: Parallel resistance (�), Id1: Recombinationcurrent.

Modeling of Transformer

The shunt branch is the main source of harmonics in trans-former. These harmonics are produced due to nonlinearcore loss resistance, nonlinear inductance and frequencydependent resistances of primary and secondary windings.Fig. 3 represents the transformer equivalent circuit con-taining phase shifter and electrical equivalents of harmonicproducing elements. Moreover, the generated harmonicsalso depends on the phase shifting and transformer windingconnections [18, 19].

Where,

R1, R2 Primary and secondary winding resistance rep-resenting copper losses,

X1, X2 Primary and secondary winding reactance repre-senting leakage flux,

Lm Magnetizing reactance, representing core fluxRm Magnetizing resistance representing Iron loss in

the coreRf1, Rf2 Primary and secondary winding resistances

depending on frequency, represents skin effectN1: N2 Ideal transformer turns ratio

The equivalent π harmonic model of transformer can bedeveloped as shown in Fig. 4 [20–22].

Where, Y(h)A , Y

(h)B , Y

(h)C are equivalent admittance of

transformers after considering all the elements and har-monic producing branches. The harmonics admittancematrix for complete transformer is expressed in Eq. 2.

[Y (h)xy(tr)] =

[(Y

(h)A + Y

(h)B ) −Y

(h)A

−Y(h)A (Y

(h)C + Y

(h)A )

](2)

Modeling of Distribution Lines and Cables

Mathematical modeling of power systems in frequencyand time domain techniques employ an admittance matrixmodel of the system. For balanced system the admittancematrix is defined as [24, 25].

[Ybus] = [A] .[Yprim

][A]T (3)

In Eq. 3, Incidence matrix [A] is used to representnetwork connectivity.

An un-transposed, LV distribution feeder feeds the loadswhich are highly nonlinear and contains harmonics. In orderto analyze these conditions, a harmonic model of the powersystem network is required [23]. For non-sinusoidal oper-ating conditions the admittance matrix will be defined atharmonic frequencies. One such LV three phase, four wiresystem is shown in Fig. 5, in which the conductors are con-nected between the buses x and y. The size of the harmonicsadmittance matrix for this system will be of 4 × 4 (4), con-

Fig. 4 Transformer π equivalent harmonic model


Fig. 5 Representation of threephase four wire distribution line

sisting of self and transfer admittances between phases andneutral [26, 27, 29].

[Y (h)xy ] =

⎡⎢⎢⎢⎣

y(h)aa y

(h)ab y

(h)ac y

(h)an

y(h)ba y

(h)bb y

(h)bc y

(h)bn

y(h)ca y

(h)cb y

(h)cc y

(h)cn

y(h)na y

(h)nb y

(h)nc y

(h)nn

⎤⎥⎥⎥⎦ (4)

Modeling of Load

The harmonic power flow analysis requires equivalent cir-cuits of linear loads because they affect the resonanceconditions and provide damping at higher frequencies [30].At fundamental frequency, linear loads are modeled as con-ventional PQ and PV buses. However, shunt admittancesare used to model them at harmonic frequencies [28]. Theadmittance of a linear load connected to bus y at the hth

harmonic frequency is given in Eq. 5.

y(h)y =

⎛⎜⎝P

(1)y − j

Q(1)y

h∣∣∣V (1)y

∣∣∣2⎞⎟⎠ (5)

At the harmonic frequencies, the nonlinear loads (such asline commutated converters, arc furnace etc.) can be mod-eled as harmonic current sources and shunt admittance.The harmonic current at any bus y will be function of itsfundamental and harmonic voltages as expressed in Eq. 6.

I (h) = f hy

(V (1)

y , V (5)y , V (7)

y , V (9)y , .....V (L)

y , αy, βy

)(6)

Where, L is the maximum harmonic order, αk and βk arenonlinear load control parameters.

Harmonic Analysis Algorithm

The harmonic power flow is a reformulation of the con-ventional Newton-Raphson power flow algorithm to includenon-linear loads [31]. In this section, the conventionalNewton-Raphson algorithm is reformulated by includingthe solar PV and nonlinear loads. The solar PV can be mod-eled as a constant PQ model and negative load with currentinjecting into the node. For steady-state analysis, constantnegative PQ model of DG resources can be used [32]. Thismethod checks the power mismatch at the end of feeders and

Fig. 6 Distribution grid with solar PV integration


laterals, in order to find the harmonics and system operatingvariables of PV integrated distribution system [33, 34]. Ini-tially, the variables are arranged into a real vector Z, whichconsists of fundamental, harmonic voltages and nonlinearsolar PV elements.

[Z] =[V (1), V (5), V (7).......V (L), [�]

]T

(7)

In Eq. 7, [�] are the nonlinear parameters of solar PVand L is the maximum harmonic order. The algorithm stepsfor power flow solution are given below:

Step 1: Read the distribution networks line data and busdata. Implement the fundamental power flow analysisand compute an initial value for the fundamental busvoltage magnitudes and phase angles.

Step 2: Calculate the fundamental and harmonic currentmismatch vector for solar PV and various load buses inFig. 6.

�I(1) =⎡⎢⎣

I(1)r,1 , I

(1)i,1 , .........I

(1)r,x−1, I

(1)i,x−1,

I(1)r,x + g

(1)r,x , I

(1)i,x + g

(1)i,x , ...

I(1)r,y + g

(1)r,y , I

(1)i,y + g

(1)i,y

⎤⎥⎦

T

(8)

�I(h) =⎡⎢⎣

I(h)r,1 , I

(h)i,1 , .........I

(h)r,x−1, I

(h)i,x−1,

I(h)r,x + g

(h)r,x , I

(h)i,x + g

(h)i,x ,

I(h)r,y + g

(h)r,y , I

(h)i,y + g

(h)i,y

⎤⎥⎦

T

(9)

In Eq. 8, I(1)r,x and I

(1)i,x are the real and imaginary bus

injection currents at bus x. Superscript (1) is used for fun-damental frequency. g(1)

r,x and g(1)i,x are real and imaginary

line currents. Subscript (y) is used for corresponding businjection current at y bus. In Eq. 9, I (h)

r,x and I(h)i,x are the

real and imaginary bus injection currents at bus x. Super-script (h) is used for harmonic frequency. g

(h)r,x and g

(h)i,x

are real and imaginary line currents.Step 3: Evaluate the mismatch vector for mismatch in

power and current on each bus. Check the convergence.

�M = [�W, �I(5), .......�I (L), �I (1)]T (10)

In Eq. 10, �W is the mismatch power vector and(�I(5), .......�I (L), �I (1)

)is mismatch current vector

for harmonics including fundamental.Step 4: Evaluate jacobian matrix and calculate correction

vector.

J (h) =

⎡⎢⎢⎢⎢⎢⎣

∂�P(h)2

∂δ(h)2

∂�P(h)2

∂V(h)2

......∂�P

(h)2

∂δ(h)y

∂�P(h)2

∂V(h)y

∂�Q(h)2

∂δ(h)2

∂�Q(h)2

∂V(h)2

......∂�Q

(h)2

∂δ(h)y

∂�Q(h)2

∂V(h)y

.. .. .. ..

.. .. .. ..

⎤⎥⎥⎥⎥⎥⎦

(11)

In Eq. 11, J (h) is the jacobian matrix at harmonic fre-quency which has all entries zero for linear buses. �P

Table 1 Solar PV parameters

1 PV panel (Watt/panel) 280

2 PV panels in series 11

3 PV panels in parallel 161

4 Total No. of panels 1771

5 Volts , dc 400

6 KW, dc 500

7 Amp, dc 1240

8 Inverter, kva 600

9 Inverter, amp 800

10 Inverter, output voltage (volts) 433

and �Q are the change in real and reactive powers, w.r.tvoltage V and phase angle δ.

Step 5: Compute the bus voltage correction vector asgiven in Eq. 12. η is the number of iterations.

�Z = Z(η) − Z(η+1) (12)

Step 6: Update the vector Zas given in Eq. 13.

Z(η+1) = Z(η) − �Z (13)

Step 7: Update the real and reactive power mismatch dueto solar PV and nonlinear loads at given buses.

�P nonlineark = P

(t)k +

∑h

F(h)r,k (14)

�Qnonlineark = Q

(t)k +

∑h

F(h)i,k (15)

Table 2 Current THD in various branches

From To % THD With PV % THD Without PV

Bus1 Bus2 45.07 3.91

Bus2 Bus3 50.18 1.05

Bus2 Bus 10 49.03 1.04

Bus2 Bus 17 15.57 2.44

Bus3 Bus4 39.22 1.07

Bus3 Bus6 8.55 1.03

Bus4 Bus5 35.92 1.09

Bus4 Bus 9 9.19 1.03

Bus6 Bus 7 8.55 1.03

Bus6 Bus 8 8.56 1.03

Bus 10 Bus 11 8.99 1.03

Bus 10 Bus 12 8.99 1.03

Bus 10 Bus13 40.84 1.06

Bus 13 Bus14 9.64 1.04

Bus13 Bus 15 9.69 1.04

Bus13 Bus 16 33.3 1.09

Bus 17 Bus 18 24.66 3.4

Bus 17 Bus 19 8.05 1.72


Fig. 7 Harmonic current waveform in the branch connected between buses 2 and 3

Fig. 8 Spectrum of harmoniccurrent in the branch connectedbetween buses 2 and 3


Fig. 9 Transformer harmoniccurrent waveform

Where, k = 1, 2, 3, 4, ......x, y.In Eqs. 14–15, Pk and Qkare the total real and reac-

tive power at bus k.Fr,k and Fi,k are the total real andimaginary line powers.

Step 8: Go to step 2. Calculate the mismatch vectors againand check the convergence.

Design of Smart Distribution Grid System

The solar PV integrated smart distribution grid system ismodeled in Fig. 6. Loads are fed from an 11KV grid througha transformer of rating 1.5 MVA, 11/0.433 KV. Lateralsare feeding the loads of varying nature in the area. Table 1

Fig. 10 Spectrum oftransformer harmonic current


Table 3 Voltage THD at various buses

Bus No. % THD With PV % THD Without PV

1 0.57 0.08

2 9.81 1.28

3 10.58 1.28

4 11.28 1.28

5 13.19 1.28

6 10.48 1.28

7 10.48 1.28

8 10.48 1.28

9 11.26 1.28

10 11.08 1.28

11 11.05 1.28

12 11.04 1.28

13 11.76 1.28

14 11.74 1.28

15 11.75 1.28

16 13.67 1.28

17 10.03 2.15

18 10.25 2.61

19 10 2.14

presents the parameters of solar PV which are connected atbus 5 and 16 respectively.

Simulation Results Analysis

This section presents the extensive analysis of harmonicswith and without solar PV integration at the various busesand branches of the modeled smart distribution grid system.The branch wise comparison of total harmonic distortionsin current, with and without solar PV integration, has beenpresented in Table 2.

It is found that the harmonic distortion in current risessharply after solar PV integration. The current harmonicdistortion (%THD) in the branch connected between buses2–3 increases to a very high value of 50.18 %. The natureof such distorted current is shown in Fig. 7. Analysis ofharmonic amplitude spectrum, as shown in Fig. 8 depictsthat it contains the 5th, 7th, 11th, 13th, 17th, and 19th orderharmonics, which violates the acceptable limits as given inTable 6. The share of 5th and 7th order harmonic is more,which affects the system performance severely and needsimmediate filtering.

Harmonics makes the distribution transformer currenthighly distorted as shown in Fig. 9. Amplitude spectrumin Fig. 10 contains the 5th, 7th, 11th, 13th, 17th and 19th

order harmonics which violates the standard limits given inTable 6. Such current escalate the iron losses and reducesthe transformer efficiency, consequently derating becomesessential.

Fig. 11 Voltage waveform atbus 16


Fig. 12 Spectrum of harmonicvoltage at bus 16

The bus wise comparison of total harmonic distortionsin voltage, with and without solar PV integration, has been

Table 4 Variation in voltage due to harmonics after solar PVintegration

Bus ID Specified kV Fundamental RMS Voltage % THD %

Voltage %

Bus 1 11 100 100.0 0.57

Bus 2 0.433 97.7 98.2 9.81

Bus 3 0.433 97.6 98.1 10.58

Bus 4 0.433 97.7 98.3 11.28

Bus 5 0.433 98.1 98.9 13.19

Bus 6 0.433 96.7 97.2 10.48

Bus 7 0.433 96.5 97.0 10.48

Bus 8 0.433 96.5 97.1 10.48

Bus 9 0.433 96.5 97.1 11.26

Bus 10 0.433 97.6 98.21 11.08

Bus 11 0.433 96.2 96.8 11.05

Bus 12 0.433 96.2 96.8 1.04

Bus 13 0.433 97.6 98.3 11.76

Bus 14 0.433 97.0 97.6 11.74

Bus 15 0.433 97.3 97.9 11.75

Bus 16 0.433 98.1 99.0 13.67

Bus 17 0.433 96.7 97.2 10.03

Bus 18 0.433 96.4 96.9 10.25

Bus 19 0.433 95.4 95.9 10

presented in Table 3. Results show that with solar PV inte-gration, the THD at bus 16 rises to a very high value equal

Table 5 System power flow variations after solar PV integration

Bus ID Variation in Variation in Variation in Amp (%)

MW (%) MVAR (%)

Bus 1 97 −2 46

Bus 2 133 −3 39

Bus 3 363 −5 −128

Bus 4 0 −4 0

Bus 5 556 −8 −285

Bus 6 −1 0 0

Bus 7 −1 −1 0

Bus 8 0 −4 0

Bus 9 0 0 0

Bus 10 −2 0 0

Bus 11 0 0 0

Bus 12 −1 −2 0

Bus 13 275 −5 −58

Bus 14 −2 0 0

Bus 15 −2 0 0

Bus 16 744 −11 −442

Bus 17 −1 −1 −1

Bus 18 −1 −1 −1

Bus 19 0 0 0


Table 6 Limits of maximum harmonic current distortion inPercent,(Based on IEEE Std. 519-1992, 1993) [11]

Harmonic Orders IEEE Std. 519-1992 (%)

5 4

7 4

11 2

13 2

17 1.5

19 1.5

23 0.6

25 0.6

29 0.6

31 0.6

35 0.3

THD 5

to 13.67 % as compared to the THD value of 1.28 % with-out solar PV, Moreover, all other buses are also affectedby harmonics. A clear violation of 5 % voltage standardlimits, as given in Table 7 can be seen after solar PVintegration.

The distorted voltage waveform at bus 16 is presentedin Fig. 11. The individual voltage harmonic contributionis depicted in concerned harmonic spectrum Fig. 12. It isfound that, the harmonic spectrum contains 5th, 7th, 13th,17th, and 19th order harmonics which violates the individualharmonic distortion limits of 3 %.Moreover, these harmonicdistortions alter the value of fundamental and RMS voltagesas presented in Table 4. Therefore, a proper mitigation tech-nique is essential to filter out these harmonics and resolvethe related issues.

Table 5 presents the comparative results of harmonicpower flow variables. The variation in current is very high atbuses 5 and 16 after solar PV integration, which poses bur-den on the connecting cables and requires higher size cables.Moreover, negative variation in power flow and current isobserved at some buses. Such reverse power can affect theprotection system and false tripping of protective gears canoccur (Tables 6 and 7).

Table 7 Limits of harmonic voltage distortion at the PCC (Based onIEEE Std. 519-1992, 1993) [11]

PCC Voltage Individual Harmonic Total Harmonic

Magnitude (%) Distortion (THD)

≤ 69 KV 3.0 5.0

Conclusion

The power distribution system has a large number of non-linear loads, which generates harmonics in the system.Integration of solar PV further enhances the distortion andthereby degrades the quality of power supply. Mitigationof harmonics is possible only if their exact nature, individ-ual percentage and THD are known. Normal power flowmethod does not provide above information. In this paper,harmonic power flow approach is implemented for a solarPV integrated smart distribution system. Comparison resultsof before and after solar PV integration has been analyzed.It is observed that integration of solar PV alters the sys-tem power flow variables and increases the harmonics in thesystem beyond the prescribed limit, which is a major chal-lenge and needs to be addressed in the integration process.The grid must be able to absorb these challenges in order toachieve the smart grid objectives. The analysis presented inthis paper will be helpful for designing an electronic filteras a control solution and make the system harmonic free.

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